D varies as R and S, and inversely as t. D=12, R=3, S=20, and t=5, find D when R=15, S=4 and t=8.

A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other. We can also think of a square as a rectangle with equal length and breadth.

The area of a square is given as side².

We have,

The total amount of wood.

= 4 x 65.5

= 262 inches.

Frame:

Side = 5.25 inches

The perimeter of the frame.

= 4 x 5.25

= 21 inches

Now,

Sandbox:

The wood used for the sandbox.

= 11 x 21

= 231 inches

The remaining wood.

= 262 - (21 + 231)

= 262 - 252

= 10 inches

Thus,

The remaining wood is 10 inches.

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Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.

Here,

A cylinder has a volume of V = r2h.

As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.

The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.

Thus, you would receive one-third of the initial mass.

What would occur if you increased the radius by 1/3 in contrast to this?

Next, you would have

=> V = π[(1/3)r]2h

=> V = π(1/9)r2h

=> V = (1/9)πr2h

You would then possess 1/9 of the volume.

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

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Answer:

Step-by-step explanation:

11 -(-2) x 4

11 + 2 x 4

11 +8

= 19

The number of yards of rope she can make for the step is 3 yards

From the question, we have the following parameters that can be used in our computation:

Yards of rope per step = 1/2 yards per step

Total number of steps = 6 steps

The number of yards of rope she can make for the step can then be calculated using the following equation

The number of yards of rope = Total number of steps * Yards of rope per step

Substitute the known values in the above equation, so, we have the following representation

The number of yards of rope = 1/2 * 6

Evaluate

The number of yards of rope = 3

Hence, the number of yards of rope is 3

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Complete question

Judi is making a rope ladder. she uses 1/2 yard of rope for each step. how many steps can she make with 6 yards of rope?

In order to find the length of v in ΔUVW, we can use the Law of Sines.

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all sides and angles in the triangle. This can be expressed as:

a/sin A = b/sin B = c/sin C

Where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the angles opposite those sides.

In ΔUVW, we are given the lengths of two sides (w and v) and the measure of the angles opposite those sides (m∠W and m∠U). We can use the Law of Sines to find the length of v:

v/sin U = w/sin W

v = (w/sin W) * sin U

Substituting the given values, we get:

v = (1.4 cm / sin 63°) * sin 29°

Using a calculator, we find that v = 2.72 cm to the nearest hundredth of a centimeter. Rounding to the nearest 10th of a centimeter, we get v = 2.7 cm.

Therefore, the length of v in ΔUVW is approximately 2.7 cm to the nearest 10th of a centimeter.

If cosec (tetha) = 17/15 then cos (tetha) = 8/17

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

cosec , sine, cotangent, cosine , secant and tangent are trigonometry function.

cosec( tetha) = 1/sin(tetha)

tangent (tetha) = 1/ cot ( tetha)

sec (tetha) = 1/ cos(tetha)

cosec (tetha) = 17/15

therefore 1/sin ( tetha) = 17/15

sin( tetha ) = 15/17 = opp/ hyp

therefore using Pythagoras theorem adj² = 17²-15²

adj² = 289-225

adj² = 64

adj = √64 = 8

cos ( tetha) = adj/hyp

therefore cos ( tetha) = 8/17

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Answer:≤ sorry if it's wrong I'm not a fan of math

Step-by-step explanation:

The value of the fourth power of the expression is 1679616.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression: 6/d -10c - c, where c = -3 and d= 2

Solving the expression, we get,

6/2-10(-3)-(-3)

= 3+30+3

= 36

We are asked to find the fourth value of 36,

(36)⁴ = 36 × 36 × 36 × 36 = 1679616

Hence, the value of the expression is 1679616.

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Answer:

There will be 5 roses.

Step-by-step explanation:

Let r = the number of roses.

Total cost =

numberof Roses × price per rose AND cost of vase

Total at Kingwood's

= 1r + 20

Total at Anita's

= 3r + 10

We are looking for r (the number of roses) when the totals at either place are the same.

Set them equal to each other.

1r + 20 = 3r + 10

Subtract 1r.

20 = 2r + 10

Subtract 10.

10 = 2r

Divide by 2.

10/2 = r

5 = r

When Elijah buys 5 roses, the cost is the same at either florist.

Check:

at Kingwood's

= 1r + 20

= 1(5) + 20

=25

At Anita's

= 3r + 10

= 3(5) + 10

= 15 + 10

= 25

5 roses costs $25 at either florist.

Answer:

g(f(x)) = 4x² - 12x + 10

Step-by-step explanation:

to find g(f(x)) substitute x = f(x) ino g(x)

g(f(x))

= g(2x - 3)

= (2x - 3)² + 1 ← expand parenthesis using FOIL

= 4x² - 6x - 6x + 9 + 1

= 4x² - 12x + 10

a) The portion of the garden is made up of beef steak tomatoes is 8.

b) he Equation for beef steak tomatoes is 4/5 x (portion of tomatoes).

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Portion of Garden have Tomatoes = 2/3

and, 4/5 of the tomato plants are beefsteak tomatoes.

a) The total section in model is 15.

so, Tomatoes in the garden = 2/3 x 15

                                               = 10

and, the portion of the garden is made up of beef steak tomatoes

= 10 x 4/5

= 8 portion.

b) The Equation for beef steak tomatoes

= 4/5 x (portion of tomatoes)

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After completing the square, the solution of equation are,

⇒ x = (2 + √2i)

And, x = 2 - √2i

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ x² - 4x + 6 = 0

Completing the square as;

⇒ x² - 4x + 6 = 0

⇒ x² - 4x + 4 + 2 = 0

⇒ (x - 2)² + 2 = 0

⇒ (x - 2)² - (√2i)² = 0

⇒ (x - 2 - √2i) (x - 2 + √2i) = 0

This gives two complex solution as;

⇒ x = (2 + √2i)

And, x = 2 - √2i

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Therefore , the solution to the given problem of expression comes out to be  149-k =x be used it as its expression.

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Here,

Given :  Lena has $149

she spends k amount of money

The money left be x

=> 149-k =x

Therefore , the solution to the given problem of expression comes out to be  149-k =x be used it as its expression.

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Answer:

90 degree

Step-by-step explanation:

since the angle BAC is 90 degree, no matter the triangle is rotated, or translated , the angld of the triangle do nit change.

To illustrated this, see attached pages.

Answer:

The answer is 10.

16 - 3 = 13

10 + 3 = 13

Answer:

10

Step-by-step explanation:

Here,10+3=13

and,16-3=13

a) Let x be the number of games played and let y be the total price.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

(b)

Pin Lanes: y = 10 + 3x

Strike Lanes: y = 4 + 6x

(c) To find the number of games at which the total price is the same at both places, we can set the two equations equal to each other and solve for x:

10 + 3x = 4 + 6x

6x = 6

x = 1

So the total price would be the same if you played 1 game at both Pin Lanes and Strike Lanes.

(d) Since you want to play 4 games, you can substitute x = 4 into the equation for each place:

Pin Lanes: y = 10 + 3(4) = 22

Strike Lanes: y = 4 + 6(4) = 28

Since 4 games at Pin Lanes costs $22 and 4 games at Strike Lanes costs $28, it would be cheaper to play at Pin Lanes.

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Answer:

x= -4/19

Step-by-step explanation:

19x+4

19x+4=0

19x= - 4

x= -4/19

Answer:

1/30 of a mile per minute.

Step-by-step explanation:

8/4 = 2 miles per hour.

2/60 = 1/30 of a mile per minute.

Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

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Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

Answer:

well, both the domain, and the range can have a positive and/or negative infinity, but as long as the 2nd factor is an opposite symbol then you will have a correct answer, for instance, -infinity, and 2 could work, but if the 2 was negative then there would be a problem

Step-by-step explanation:

The length of time to build the fence is 8 hours

From the question, we have the following parameters that can be used in our computation:

Length of the fence = 1 1/3 miles

Rate of building = 1/6 miles per hour

The length of time to build the fence is then calculated as

Length of time = Length of the fence/Rate of building

Substitute the known values in the above equation, so, we have the following representation

Length of time = (1 1/3 miles)/(1/6 miles per hour)

Evaluate the quotient

This gives

Length of time = 8 hours

Hence, the time taken is 8 hours

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Answer:

1/2 or 0.5 inches per hour

Step-by-step explanation:

5 divided by 10 will get you this answer

Answer:

  x = 7

Step-by-step explanation:

You want to know the value of x when the base of a triangle measures 5x+35, and its midsegment measures 35.

The base of the triangle is twice the length of the midsegment, so you have ...

  5x +35 = 2(35)

  5x = 35 . . . . . . . . . . subtract 35

  x = 7 . . . . . . . . . . divide by 5

__

Additional comment

The midsegment joins the midpoints of the sides of the triangle.

In more formal terms, the smaller triangle is similar to the larger one with a scale factor of 1/2. That means the parallel segments are related by that scale factor of 1/2: (1/2)(5x +35) = 35.

Answer:

  y = 2x -3

Step-by-step explanation:

You want the equation of the line through the points (-1, -5) and (2, 1).

The slope of the line is given by ...

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-5))/(2 -(-1)) = 6/3 = 2

The y-intercept of the line can be found from ...

  b = y -mx

  y = -5 -2(-1) = -3

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . . . line with slope m and y-intercept b

Using our found values, the equation is ...

  y = 2x -3 . . . . . . . . line with slope 2 and y-intercept -3

Answer:

1332

[tex]7x))742 \sqrt[ \sqrt[241]{?} ]{?} [/tex]

Answer:

Refer to the step-by-step.

Step-by-step explanation:

[tex]Given:\\ \lim_{x\to \22} \frac{1}{1-x}[/tex]

Plug in the value of 2 in for x. We get,

⇒ [tex]\frac{1}{1-(2)}[/tex] ⇒ [tex]\frac{1}{-1}[/tex] ⇒ -1

So,  [tex]\\ \lim_{x\to \22} \frac{1}{1-x} = -1[/tex]

Cannot be determined.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here  5 pizzas and 2 bags of chips cost $55 and 10 pizzas and 4 bags of chips cost $95

let the cost of one pizza be p and a bag of chips be c then we construct the following linear equations:

5p+2c=55

10p+4c=95

Clearly the equations are colinear but 10p+4c≠110=1(5p+2c0

and thus two lines don't have a unique solution.

Hence, the cost cannot be determined as the two equations have no solution in common.

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On solving the provided question, we can say that - the linear equation

y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y=mx+b

x=gallons of fuel

y=total weight of plane including fuel

m=slope=6.4

b=weight of plane, no fuel....a constant to be calc'd

[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]

82gallons fuel is 2424.80 lbs

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Answer: He was 32 years old 8 years ago, than a) x-40 b) x-24 c) 40-x d) 24-x e) 24+x

Step-by-step explanation:

Mario was '40 - x' years old when he was 'x' years old.

If he was 32 years old, 8 years ago, then he is 40 now as (32+8) equals 40.

If he is 40 years old now, then he was '40 - x',  x years ago.

Hence, '40 - x' is the answer to this sum.

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Answer: 3/-2

Step-by-step explanation:

3/-2 and -3/2 mean the same thing and give same result if we divide the numerator by denominator.

hope that helps...